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  2. Odds - Wikipedia

    en.wikipedia.org/wiki/Odds

    These definitions are equivalent, since dividing both terms in the ratio by the number of outcomes yields the probabilities: : = (/): (/). Conversely, the odds against is the opposite ratio. For example, the odds against a random day of the week being during a weekend are 5:2.

  3. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

  4. Outcome (probability) - Wikipedia

    en.wikipedia.org/wiki/Outcome_(probability)

    In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. [2]

  5. Probability theory - Wikipedia

    en.wikipedia.org/wiki/Probability_theory

    Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.

  6. Sample space - Wikipedia

    en.wikipedia.org/wiki/Sample_space

    The outcomes must be collectively exhaustive, i.e. on every experiment (or random trial) there will always take place some outcome for {,, …,}. [ 6 ] The sample space ( Ω {\displaystyle \Omega } ) must have the right granularity depending on what the experimenter is interested in. Irrelevant information must be removed from the sample space ...

  7. Classical definition of probability - Wikipedia

    en.wikipedia.org/wiki/Classical_definition_of...

    The classical definition of probability assigns equal probabilities to events based on physical symmetry which is natural for coins, cards and dice. Some mathematicians object that the definition is circular. [11] The probability for a "fair" coin is... A "fair" coin is defined by a probability of... The definition is very limited.

  8. Probability measure - Wikipedia

    en.wikipedia.org/wiki/Probability_measure

    In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable additivity. [1] The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume ) is that a probability measure must ...

  9. Probability interpretations - Wikipedia

    en.wikipedia.org/wiki/Probability_interpretations

    The classical definition of probability works well for situations with only a finite number of equally-likely outcomes. This can be represented mathematically as follows: If a random experiment can result in N mutually exclusive and equally likely outcomes and if N A of these outcomes result in the occurrence of the event A , the probability of ...